PID controller: dummy questions

Yes - P goes to zero, and I /stabilises/ to a value of output that results in a steady state.

If you overshoot - perhaps I has built up too much - the error term will be negative, so the I term will decrease (but remain positive for a while), while the P term will be negative.

That works for some kinds of systems. In other systems, you might have gravity or a spring that means keeping the same position requires a constant small force - you get that from the I term.

In this case, the I term will be zero at the perfect stable spot. But it could well be non-zero while moving - a P term alone rarely gets you to the target. (Imagine you are near the target. The P term might give too low a force to overcome the static friction and move the bar - then the I term will build up until things are moving.)

Yes.

In any regulation system, you have a balance between reacting quickly to changes and minimising overshoot and oscillations. The D term can be helpful in reducing these unwanted effects.

You'll never get to the target that way. Maybe that's okay, and you'll get close enough. Sometimes overshoot must be avoided at all costs, other times it is merely a mild inconvenience - there is no single answer to all regulation problems.

And pure PID is just one way to regulate a system. You can use variations or ad-hoc methods (such as P regulation, but using an artificial setpoint beyond the real target, or applying a break when you hit the target), or you can use completely different regulation techniques.

The error is *after* all three PID factors are added. The I factor reduces the error. If it reduces the error to zero, the I term stops increasing.

In real life terms, consider this: you want to heat a pot of water to a slow boil. You turn on the stove, at first a lot as a "guess" but as the pot approaches the boiling you turn the heat down (P term). Eventually you have to start tweaking the heat up a bit to bring the temperature up, this is the I term. As you approach the right temp, you tweak in smaller increments, until you're there.

Error is 30.

Better example: when the heat gets to 45 degrees (error=5) the P term has been reduced enough that the water doesn't get any warmer. If the water were to warm up, the heat would be reduced, and it would cool again. You've reached steady state, and this is as close as the P term can get you. This happens relatively quickly. Let's say the P term is providing 500 watts at this point.

Now, you need a little more heat to make up the difference.

The I term sees the small remaining error, and slowly adds more heat, until the temperature slowly climbs to the set point. The I term might be adding another 5 watts or so

And the error quickly jumps up, the P term immediately reacts. The I term slowly starts rising again. More heat pours in. The temperature might rise past the set point, but then the error is *negative* and the I term slowly goes down until it's back where we started.

You're missing that if the I term keeps increasing, eventually the water will be too hot, the error negative, and that reduces the I term again.

It's like the pot on the stove. You turn the heat up until the water is the right temperature, but if you *keep* turning the knob up, the water becomes too hot, and you have to turn the knob back down again.

The motor situation where you want 0 signal to hold at the desired set point, basically implies that the system has an integrator in its response. (A pole at zero). With the motor that is because the input Voltage determines the Speed of the motor, and the motor mechanics integrates that speed to become a position, which is the thing that is being controlled. Such a system may not need an integral term for 0 error (because the plant provides that integral term).

On the other hand, if there is a bit of force on the motor (maybe gravity) and with zero input, the system slides of the control point, so we need to add a bit of voltage to provide some torque to counter that force, that brings back the need for the integral loop to provide that balancing voltage.

One issue with your P only controller for position, is that as you get close, you slow down, so you close slower, and slower, so it takes a while to get to where you want (theoretically, forever, as you will close exponentially). You can make the loop faster by raising P, but at some point, the gain gets too high, and other dynamics or time delays get in the way and the system may mal-perform.

PID loops, when properly tuned, can get you closer faster when you tune the system to be critically damped, the key being that you let the PI terms give you a higher starting gain, but then the damping term backs that off giving you more gain at slow speeds, which handles the base error, and less gain at high frequencies where the instabilities live.

As to changing parameters, yes that can be done, and that gets you into the domain of non-linear control. Such system can be harder to think about or analyze, and it can introduce strange phenomenon like limit cycles. I would probably not have a sharp change of values at 0 error, as that would likely be the nominal operating point, so very apt to create limit cycles. You might either gradually adjust the parameters as you go negative, or have a break-point at a certain amount of error that you don't normally expect to reach.

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Not "if" but just "how much" I will cause overshoot. The I term is an osci llator with P as a damping factor.

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Not correct. This design incorporates the integrator into the mechanism. Position is the integral of velocity which is proportional to the output of the controller. So the additional integrator is not required in the contr oller. But the P term will get to the end position because there is non-id eal behavior in moving the bar because of it's mass. So velocity is not pe rfectly proportional to the control output.

This is why the theory is so hard to manage in real world situations. Ther e are many, many nonidealities. While many of them won't have a significan t impact on the controller, some may and it can be hard to know which need to be factored in.

I'm working on a PID simulation in LTspice. I thought I'd use the "univers al op amp" as an ideal device, but I guess I should have read the data shee t first... lol. I should have something working later in the day.

Working on lunch at the moment.

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  Rick C. 

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The integral term is supposed to be a pure integral, no decay. It will only keep getting bigger if you keep having error of the same sign.

Often, limits are put on the integration, to limit the overshoot from 'windup' as the system tries to get close or special rules to hold the integrator when the P-D part of the loop is driving hard.

On Saturday, June 27, 2020 at 1:10:00 PM UTC-4, Rick C wrote:

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Position is the integral of velocity which is proportional to the output of the controller. So the additional integrator is not required in the con troller. But the P term will get to the end position because there is non- ideal behavior in moving the bar because of it's mass. So velocity is not perfectly proportional to the control output.

ere are many, many nonidealities. While many of them won't have a signific ant impact on the controller, some may and it can be hard to know which nee d to be factored in.

rsal op amp" as an ideal device, but I guess I should have read the data sh eet first... lol. I should have something working later in the day.

I didn't like the op amp circuits too many components. Here is an LTspice simulation with voltage sources as amplifiers, simpler.

The ringing of the controlled quantity can be managed by "tuning" the ratio of the proportional section to the integral section. Too little P term an d ringing starts. Too much P term and the response is slow. I tried it wi th no P term and the ringing is all you see practically. Ramping down both together rounds the corners of the response. Ramping up both together sha rpens the corners crisply.

PID.asc

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PID.plt

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  Rick C. 

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I've found Tim Wescott's website helpful

Especially this:

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Best wishes, 
--Phil 
pomartel At Comcast(ignore_this) dot net